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\section{\usemenu{slacpub7245::context::slacpub7245001}{Introduction}}\label{section::slacpub7245001}
A precise determination of the CabibboKobayashiMaskawa
matrix element
$V_{ub}$ is an important step for constraining the unitarity triangle.
Therefore, it
poses a challenge for both theory and experiment~\cite{1}.
Traditionally, $V_{ub}$
has been extracted from the energy spectrum of the
charged lepton in inclusive
semileptonic $B$ decays
$B \rightarrow X_u \ell \nu$
above charm threshold, i.e.,
for lepton energies $E_\ell$ above $(m_B^2  m_D^2)/(2m_B)
\approx 2.3$ GeV~\cite{2,3}~\footnote{
We will discuss the impact on the determination of $V_{ub}$
from the recent CLEO measurements of the corresponding
exclusive channels
$B \to (\pi,\rho,\omega) \, \ell \nu$
\cite{4,5} later.}.
As the kinematical endpoint for semileptonic $B$ decays is at
$E_\ell=(m_B^2  m_\pi^2)/(2 m_B) \approx 2.6$ GeV,
the pure $b \rightarrow u \ell^ {\overline \nu}$ transition
extends over a
relatively narrow window of about 300 MeV, accepting only
a fraction of approximately 10 \% of the total sample of charmless
$B$ decays. Theoretically, the lepton energy spectrum may be calculated
from firstprinciple QCD. Using the
tools of the operator product expansion (OPE) and
heavyquark effective field theory~\cite{6},
one can construct a systematic expansion of
the lepton spectrum in powers of $\L/m_b$, where $\L$
is a typical lowenergy scale of QCD
\cite{7}.
However, the relevant
lepton energy window from which $V_{ub}$
can be extracted lies to a large extent in
the socalled endpoint region
which extends from the parton model maximum
at $E_\ell=m_b/2$ up to the hadronic maximum at
$(m_B^2  m_\pi^2)/(2m_B)$. It is therefore described by genuinely
nonperturbative contributions.
The difficulty arises from the fact~\cite{8}
that, close to the partonic endpoint,
the expansion parameter is no longer $\L/m_b$, but $\L/(2m_bE_\ell)$.
Thus, the theoretical prediction becomes
singular when the lepton energy approaches the parton model endpoint;
formally, these singularities manifest themselves in delta functions
and derivatives of delta functions concentrated at the partonic
lepton energy endpoint $m_b/2$. In addition, this region
is plagued by large perturbative Sudakovlike double
logarithms \cite{9,10,11} as well as by small instanton
effects~\cite{12}.
Therefore, in a large part of the lepton energy region in which
the extraction of $V_{ub}$ is kinematically possible,
a full resummation of Sudakovlike double logarithms~\cite{10} and
power corrections~\cite{13} becomes necessary.
In view of the theoretical and experimental difficulties
just mentioned, it is desirable to look for other methods.
As an alternative,
we propose to extract $V_{ub}$ from the
hadron energy spectrum in the inclusive charmless
semileptonic $B$ decays $B \to X_u \ell \nu$.
Simple kinematical considerations support why this proposal
is viable. As the charmed final state
threshold is at the $D$meson mass,
the maximal hadron energy window for
charmless semileptonic $B$ decays is given by the range
$m_\pi \le E_{had} \le m_D$; this window is much wider
than the corresponding kinematical
window for the lepton energy distribution
discussed above, and as we will see later, a much larger fraction
of the $B \to X_u \ell \nu$ events becomes accessible,
leading to improved statistics.
Of course, the theoretical problems addressed
in the discussion of the lepton endpoint spectrum are also
present in principle in the hadron
energy spectrum~\cite{14,15},
but to a much lesser extent in the kinematical region relevant
for the extraction of $V_{ub}$.
Indeed, up to perturbative QCD corrections, the region around
$E_{had}=m_b/2$ is also fully dominated by nonperturbative effects,
quite in analogy to the lepton energy endpoint region.
Fortunately, this region is well above the
charmed hadron final state threshold lying
outside the region we are interested in.
At the lower end of the hadron energy, $E_{had} \approx 0$,
the hadronic mass ranges over a narrow window
$0 \le m_{had}^2 \le E_{had}^2$, hence, the OPE breaks down again.
This region can be avoided by applying a lower cut to the
hadron energy; we choose the value 1 GeV.
This relatively high lowercut has the advantage that a wide
range of invariant hadronic masses contributes
to the hadron energy spectrum; quarkhadron duality, which we
implicitly assume in our treatment for the inclusive
$B \to X_u \ell \nu$ decay,
is then expected to work well. Even after this cut at 1 GeV
is made, we are still left with an ample hadron energy window
ranging from 1 GeV to $m_D$.
These features in principle make investigations with hadron
energy spectra more reliable than with lepton energy spectra.
Experimentally, the hadron energy spectrum in semileptonic $B$ decays
may be measured schematically as follows:
Working at the $\Upsilon(4S)$ resonance,
which decays into $B \bar B$, one requires one of the $B$mesons to
decay semileptonically and the other one hadronically. In the case of
a symmetric $B$factory, like CLEO, the energy of the hadrons stemming
from the semileptonically decaying $B$meson can be obtained by
measuring the total energy of all the hadrons in the final state
and then subtracting $m_{\Upsilon(4S)}/2$.
In case of asymmetric $B$ factories, the hadron
energy spectrum is harder to measure. One way is
to reconstruct in a first step the whole $\Upsilon(4S)$ decay
in its rest frame and then perform the analysis just described
for the symmetric case.
To perform the corresponding boost,
one has to measure precisely
both the energy and the momentum
of each final state hadron, which requires accurate particle
identification.
The remainder of this paper is organized as follows. In section 2
the calculation of the hadron energy spectrum is presented.
We utilize two methods to account for the boundstate effects.
The first one, discussed in section 2.1, uses the Altarelli et al.
(ACCMM) model~\cite{10} of the $B$meson and
the second one, presented in 2.2, is based on the heavyquark effective
field theory (HQET)~\cite{8}.
In both treatments, the perturbative
$O(\a_s)$ corrections are taken into account.
In section 3 the extraction of $V_{ub}$ and its theoretical
errors are discussed.
Finally, in section 4 we give a brief
summary together with some comments on the experimental possibilites.
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